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Introduction to Electrodynamics (3rd Edition)

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ELECTRICITY AND MAGNETISM I HOMEWORK 13: GRIFFITHS 7.1,5,7,10,13 MIKE WININGER Problem 1 (Griffiths 7.1: Concentric Metal Shells with Conducting Interior.) . . Two concentric metal spherical shells, of radius a and b, respectively, are separated by weakly conducting material of conductivity σ . a) If they are maintained at a potential difference V, what current flows from one to the other? b) What is the resistance between the shells? c) Exploit the geometry ( b a ) to determine the current between two metal spheres, each of radius a, immersed deep in the sea and held far apart if the potential difference between them is V. a) Between the shells, potential difference is V. What is the current? **Note Field between the shells is given by E = 1 4 π 0 Q r 2 ˆ r I = Z J · d a = σ Z E · d a = σ 1 4 π 0 Q r 2 4 πr 2 = 0 . b) What is the resistance? V = - Z a b E · d l = - 1 4 π 0 Q Z a b 1 r 2 = - Q 4 π 0 » 1 b - 1 a = Q 4 π 0 » 1 a - 1 b . V = IR R = V I Q 4 π 0 » 1 a - 1 b 0 σQ = » 1 a - 1 b 1 4 πσ = 1 4 πσab [ b - a ] c) What is the current in the sea?
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